第一道 (ay+bx)^3+(ax+by)^3-(a^3+b^3)(x^3+y^3)

第二道(a^2-3a+2)x^2+(2a^2-4a+1)xy+(a^2-a)y^2

手机党伤不起T.T

第三道 x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)

(ay+bx)^3+(ax+by)^3-(a^3+b^3)(x^3+y^3)
=(ay+bx+ax+by)[(ay+bx)²+(ax+by)²-(ay+bx)(ax+by)]-(a+b)(a²+b²-ab)(x+y)(x²+y²-xy)
=(a+b)(x+y)(a²y²+b²x²+2abxy+a²x²+b²y²+2abxy-a²xy-b²xy-abx²-aby²)
-(a+b)(x+y)(a²+b²-ab)(x²+y²-xy)
=(a+b)(x+y)(a²y²+b²x²+2abxy+a²x²+b²y²+2abxy-a²xy-b²xy-abx²-aby²-a²x²-a²y²+a²xy
-b²x²-b²y²+b²xy+abx²+aby²-abxy)
=(a+b)(x+y)(3abxy)
=3abxy(a+b)(x+y);

(ay+bx)^3+(ax+by)^3-(a^3+b^3)(x^3+y^3)
=@￥%*&……%￥#*）——（*&……#%……&……（%%#%YT&^*&#%#^
这就是真相和答案，LZ懂了吗


(a^2-3a+2)x^2+(2a^2-4a+1)xy+(a^2-a)y^2
=(a-1)(a-2)x²+[2(a-1)²-1]xy+a(a-1)y²
=[(a-1)x+ay][(a-2)x+(a-1)y]
=(ax-x+ay)(ax-2x+ay-y);